Abstract

Knots are commonly found in nearby planetary nebulae (PNe) and star-forming regions. Within PNe, knots are often found to be associated with the brightest parts of the nebulae and understanding the physics involved in knots may reveal the processes dominating in PNe. As one of the closest PNe, the Helix Nebula (NGC 7293) is an ideal target to study such small-scale (∼300 au) structures. We have obtained infrared integral spectroscopy of a comet-shaped knot in the Helix Nebula using the Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) on the Very Large Telescope at high spatial resolution (50–125 mas). With spatially resolved 2-μm spectra, we find that the H2 rotational temperature within the cometary knots is uniform. The rotational-vibrational temperature of the cometary knot (situated in the innermost region of the nebula, 2.5 arcmin away from the central star) is 1800 K, higher than the temperature seen in the outer regions (5–6 arcmin from the central star) of the nebula (900 K), suggesting that the excitation temperature varies across the nebula. The obtained intensities are reasonably well fitted with 27 km s−1 C-type shock model. This ambient gas velocity is slightly higher than the observed [He ii] wind velocity of 13 km s−1. The gas excitation can also be reproduced with a photon-dominant region (PDR) model, but this requires an order of magnitude higher ultraviolet radiation. Both models have limitations, highlighting the need for models that treat both hydrodynamical physics and the PDR.

1 INTRODUCTION

In recent years, it has become clear that knots of dense material are common in nebulae, including planetary nebulae (PNe; e.g. O'Dell et al. 2002) and star-forming regions (e.g. McCaughrean & Mac Low 1997). In one of the best-studied PN case, that of the Helix Nebula (NGC 7293), knots in the inner regions have a comet-like shape (O'Dell & Handron 1996) and are thus known as cometary knots. The Helix Nebula is estimated to contain more than 20 000 cometary-shaped knots (Meixner et al. 2005). The apparent commonality of occurrence in PNe of these knots has led to the assertion that all circumstellar nebulae are clumpy in structure (e.g. O'Dell et al. 2002; Speck et al. 2002; Matsuura et al. 2005b). As knots occupy the brightest parts of the PNe, understanding their physical nature is essential to understanding the dominant physics governing the nebula.

The origin of these knots remains unknown. The knots' form is also disputed: they may have been present during the preceding asymptotic giant branch (AGB) phase (e.g. Dyson et al. 1989), or only have formed during the PN phase. The suggested formation mechanisms fall into two main scenarios. First, photoevaporation from condensations which pre-exist in the circumstellar envelope was considered. Speck et al. (2002) suggest that the ultraviolet (UV) radiation from the central star heats the surface of a condensation, emitting Hα and H2 on the facing side. Secondly, the interaction of a fast stellar wind with the slowly expanding AGB wind, during the early stage of PN phase, has been considered (e.g Vishniac 1994; Pittard et al. 2005; García-Segura et al. 2006). Pittard et al. (2005) found that cometary knots may be formed through instabilities where a supersonic wind impacts a subsonic wind.

In addition to being seen as inhomogeneities within the ionized gas emission from nebulae, the knots also contain molecular gas (Speck et al. 2002, 2003). This yields a potential clue to their origin. Redman et al. (2003) argued that some molecular species formed in the AGB atmosphere can survive if molecules are shielded in clumps from UV radiations by extinction. However, if the knots (re-) form during the ionized PN phase, the earlier AGB molecules were photodissociated, and the molecules re-form within the knots, under conditions of relatively low density and higher UV intensity compared to the AGB wind. In these conditions, only simple molecules are expected to be present (Woods 2004).

Using seeing-limited observations (1.2 arcsec) of the H2v= 1–0 S(1) line in a single knot, Huggins et al. (2002) found H2 gas in both the head and the tail of the knot, following the distribution of ionized gas traced by Hα and [N ii]. In contrast, CO thermal emission was found to emanate only from the tail. Higher angular resolution images obtained with HST (Meixner et al. 2005) resolved the globular H2 emission into crescent-shaped regions. With these previous studies, it is not clear whether the hydrogen molecules and ionized gas are co-located within the head or spatially separated.

The excitation mechanisms for molecular hydrogen in PNe have long been controversial, with contention between fluorescent/thermal excitation in photon-dominant regions (PDRs) and shock excitation. Tielens & Hollenbach (1985) and Black & van Dishoeck (1987) showed that vibrationally excited H2 (by far-UV pumping) traces the surface of dense regions in the process of becoming photoionized. On the other hand, molecules can form in a post-shock region (Neufeld & Dalgarno 1989), and H2 can be excited by shocks (Beckwith et al. 1980; Hollenbach & McKee 1989). The cooling region after the shock can be resolved if it is a C-type (continuous) shock, but the region is too small to be resolved for J-type (jump) shocks. A comparison of models with spatially resolved spectra, which covers multiple line ratios, will help to understand the excitation mechanism of H2.

The Helix Nebula (NGC 7293) is one of the nearest PNe, with a largest diameter of more than half a degree (Hora et al. 2006) and a parallax distance of 219 pc (Harris et al. 2007). Because of its distance, small-scale structures inside the nebula are well resolved and this nebula is used as a proxy to understand the structures found in PNe.

We have observed a cometary knot in the Helix Nebula, using the adaptive-optics-assisted, near-infrared integral field spectrometer on the Very Large Telescope (VLT). We have achieved 50–100 mas spatial resolution. Our data provide the first spatially resolved spectra within a knot at 2 μm and further this is the highest spatial resolution image + spectra of this PN at this wavelength. Our observations of H2 spectral line ratios allow us to derive the excitation temperatures within the knot, as well as the possible excitation mechanisms of H2.

2 OBSERVATIONS AND ANALYSIS

A knot in the Helix Nebula was observed by the Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI; Eisenhauer et al. 2003; Bonnet et al. 2004) installed at the Cassegrain focus of the VLT. The grating for the K band was used. The wavelength band of the grating was mapped to the 2048 pixel detector in the dispersion direction. We used two plate-scales: the spatial resolutions are 125 × 250 and 50 × 100 mas2. For all of the observations, a nearby star forumla was used as an Adaptive Optics (AO) guide star. The spatial resolution is usually determined by the pixel-scale while using the 125 × 250 mas2 plate-scale (i.e. the images are undersampled), while for the 50 × 100 mas2 scale both the corrections of the AO system and the pixel-scale are important. The spectral resolutions λ/Δλ are 4490 and 5090 for the 125 × 250- and 50 × 100-mas2 cameras, respectively. The observing log is summarized in Table 1. The coordinates of our target knot K1 are forumla (J2000) measured from the data used by O'Dell, McCullough & Meixner (2004). This knot is noted as ID 6 in Meaburn et al. (1998) and is about 2.5 arcmin away from the central star (Fig. 1). It is located at the inner rim of the ring-shaped nebula filled with cometary knots.

Table 1

Observing log.

Target Pixel-scale of the camera (mas2Pixel-scale in reduced data (mas2Telluric standard 
Exposure time Name Spectral type K maga 
K1 125 × 250 125 × 125 300 s × 10 600 s × 10 Hip 115329 G2V 7.552 ± 0.017 
50 × 100  50 × 50 600 s × 10 Hip 023422 G2V 7.862 ± 0.017 
Target Pixel-scale of the camera (mas2Pixel-scale in reduced data (mas2Telluric standard 
Exposure time Name Spectral type K maga 
K1 125 × 250 125 × 125 300 s × 10 600 s × 10 Hip 115329 G2V 7.552 ± 0.017 
50 × 100  50 × 50 600 s × 10 Hip 023422 G2V 7.862 ± 0.017 

aK mag: K′-band magnitudes from 2MASS.

Figure 1

The location of the cometary knot K1 is plotted on the F658N ([N ii]+ Hα) image (O'Dell et al. 2004), together with the AO guide star. The star symbol indicates the place of the central star.

Figure 1

The location of the cometary knot K1 is plotted on the F658N ([N ii]+ Hα) image (O'Dell et al. 2004), together with the AO guide star. The star symbol indicates the place of the central star.

The observing run was carried out on the first-half nights from 2005 November 2 to 4. The sky was clear on November 3, with occasional thin cloud passing on November 2 and 4. The telluric standards were observed immediately after the target. The telluric standard stars were used for flux and spectral-response calibration, as well as for the measurements of the point spread function (PSF). Model spectra from Pickles (1998) are used as template spectra for the telluric standard stars. The wavelength resolution of the model spectra is 4000 only, but we assume that this difference in wavelength resolution is not critical for our analysis of the emission lines.

The field of view was slightly jittered to minimize the influence of bad pixels. The sky level was measured at +10 arcmin away in the declination direction, which is outside the bright part of the nebula. Some residual of the sky level was left, and we use the integral field to remove the residual sky level.

The European Southern Observatory (ESO) data-reduction pipeline for SINFONI on GASGANO (Modigliani et al. 2007) was used. Distortion-correction and flat-correction were adopted. Wavelength-calibration used the Ne and Ar wavelength lamps, linearly interpolated throughout the entire wavelength coverage. After the data reduction with GASGANO, the final pixel was resampled to a 125 and 50 mas scale for 125 × 250- and 50 × 100-mas2 plate-scale images, respectively.

The absolute flux-calibration has some uncertainty, due to the possibility of occasional thin cirrus (up to 0.2 mag) and the generic difficulty in the calibration of diffuse intensity using an AO-assisted point source. We reduced two 125-mas target spectra using two different exposure times independently, and the final spectra and images were obtained by averaging these two data sets. The average of our measured flux over 2 × 2 arcsec−2 is 1.2 × 10−4 erg s−1 cm−2 sr−1. Speck et al. (2002) gives the intensity of K1 at H2v= 1–0 S(1) as ∼5–10 × 10−5 erg s−1 cm−2 sr−1; the knots are not fully resolved (2 arcsec pixel−1) and the flux of this knot is close to the detection limit (∼1 × 10−4 erg s−1 cm−2 sr−1). A knot in the outer regions of the Helix Nebula, with a similar flux level to our knot in Speck et al. (2002)'s measurements, was observed by Meixner et al. (2005). They find a surface brightness of H2 of ∼1 × 10−4 erg s−1 cm−2 sr−1. We conservatively adopt a systematic calibration uncertainty of 50 per cent. Further, the sky condition affects the correction of the atmospheric transmittance, especially shortward of 2 μm and longward of 2.4 μm, due to the variation in terrestrial H2O. The relative intensities of lines below 2.0 μm and above 2.4 μm have an error of ∼30 per cent. We ignore the extinction at 2 μm; as discussed later, the extinction affects the absolute intensity less than 5 per cent (Aλ=2.128 μm= 0.05 mag).

3 DESCRIPTION OF THE DATA

3.1 Morphology

Fig. 2 shows the image of the cometary knot K1 as seen in the three strongest H2 lines. The knot shows an elongated head with a narrower tail. The brightest emission is found in a crescent near the tip of the head. The crescent ends in two linear segments, indicated by the dotted lines in Fig. 3 on the 2.12 μm v= 1–0 S(1) image. These segments are not co-aligned and deviate from the direction of the narrower tail. Overall, this gives the impression of a ‘tadpole’ shape, as opposed to the cylindrical shape favoured by O'Dell & Handron (1996), although in either case the overall shape is largely axisymmetric. Both the linear segments and the tail are brighter on the eastern side of the knot.

Figure 2

Images of the cometary knot K1, taken by the 250-mas camera. The PSF at 2.12 μm is found in (d). The direction of the central star is marked in (c).

Figure 2

Images of the cometary knot K1, taken by the 250-mas camera. The PSF at 2.12 μm is found in (d). The direction of the central star is marked in (c).

Figure 3

Annotated 2.12-μm image of the knot K1 (see the text for details).

Figure 3

Annotated 2.12-μm image of the knot K1 (see the text for details).

The peak emission is located slightly behind the tip (Fig. 3). There is a faint nebulosity around the bright head. This faint nebulosity appears not to be the wing of the PSF. The faint halo extends along the linear segments where the peak emission is much fainter. The higher resolution image (50 mas pixel−1) in Fig. 4 also shows this faint nebulosity, suggesting that at least part of this faint nebulosity is real.

Figure 4

Image of the cometary knot K1, taken with the 100-mas camera. The PSF at 2.12 μm is found in (c).

Figure 4

Image of the cometary knot K1, taken with the 100-mas camera. The PSF at 2.12 μm is found in (c).

The apparent diameter at the head is about 2.5 arcsec including the faint rim, while the diameter decreases to about 2 arcsec along the tail (Fig. 5). The transition from the linear segment to the narrower tail is visible as a kink, 2.8 arcsec from the head on the east side. It is less clearly visible on the west side.

Figure 5

Cross-cut of Fig. 2 along the radial axis, whose intensity is scaled to the maximum intensity of the knot. Approximate locations of cuts are indicated on the left-hand panel. The data are smoothed with a 250-mas bin along the long axis of the knot. The intensity peaks on the east side (right-hand side in this figure) of the knot are marked with the stars in each panel. The bottom panel shows the cross-cut of the telluric standard (bold line), airy disc for 8.2 m circular aperture (thin solid line), and pixel size (125 and 250 mas; thin dashed lines). The spatial resolution is determined by the pixel-scale (sampling rate). The star marks traces that the head is widened until the distance d= 2.0 arcsec and then narrowing follows d > 2.5. Tail of the PSF is less than 10 per cent of the peak at 0.5 arcsec.

Figure 5

Cross-cut of Fig. 2 along the radial axis, whose intensity is scaled to the maximum intensity of the knot. Approximate locations of cuts are indicated on the left-hand panel. The data are smoothed with a 250-mas bin along the long axis of the knot. The intensity peaks on the east side (right-hand side in this figure) of the knot are marked with the stars in each panel. The bottom panel shows the cross-cut of the telluric standard (bold line), airy disc for 8.2 m circular aperture (thin solid line), and pixel size (125 and 250 mas; thin dashed lines). The spatial resolution is determined by the pixel-scale (sampling rate). The star marks traces that the head is widened until the distance d= 2.0 arcsec and then narrowing follows d > 2.5. Tail of the PSF is less than 10 per cent of the peak at 0.5 arcsec.

3.1.1 H2 emission from the surface of knots

The deconvolved image (Fig. 6) shows a limb-brightened head of the knot. Within the head there may be an H2 empty region. Fig. 7 shows the radial cross-section of the head 1 arcsec inside from the brightest point. The intensity at the mid-point is about 65 per cent of the peak in the raw image and about 40 per cent in the deconvolved image. To demonstrate the shape, we modelled the radial profile in two dimensions, assuming a thin ring with a large hollow area inside (Figs 7b and c). The diameter of the circular ring is 1.5 arcsec. The density structure of the ring is assumed to be a Gaussian with a width of 0.075 arcsec. The radial cut in the deconvolved image is reasonably well reproduced by this model (Fig. 7a). The H2 emitting region is probably a very thin surface of the knot, except at the tip.

Figure 6

Deconvolved image at 2.12 μm. A faint emitting region at the rim near the crescent is found, as well as narrowing of the tail.

Figure 6

Deconvolved image at 2.12 μm. A faint emitting region at the rim near the crescent is found, as well as narrowing of the tail.

Figure 7

(a) Cross-cut of the observed intensity at 2.12 μm and PSF-deconvolved profile along the radial direction in the head. The intensities are normalized at the peak. The location is 1 arcsec away from the brightest tip. Model profile in panel (a) is to demonstrate a hollow shape in the projected image if the knot is seen from the central star (panel b) with input parameters of the shape (panel c).

Figure 7

(a) Cross-cut of the observed intensity at 2.12 μm and PSF-deconvolved profile along the radial direction in the head. The intensities are normalized at the peak. The location is 1 arcsec away from the brightest tip. Model profile in panel (a) is to demonstrate a hollow shape in the projected image if the knot is seen from the central star (panel b) with input parameters of the shape (panel c).

3.1.2 Comparisons with HST[N ii] and [O iii] images

Fig. 8 shows the image of the knot K1 at 2.12 μm H2v= 1–0 S(1), with a comparison of HSTF658N (mainly [N ii] and some contribution of Hα) with F502N ([O iii]) images from O'Dell et al. (2004). The precise alignment between SINFONI and HST images is unknown, and the images were registered such that the tip of the knot is located at the same place at [N ii] and H2v= 1–0 S(1).

Figure 8

Comparison of the SINFONI 2.12-μm image and HST images. The SINFONI and HST images were aligned on the tip of the knot. Log intensity scale is used for all of the images. The size of the image is 22.3 × 8.5 arcsec2.

Figure 8

Comparison of the SINFONI 2.12-μm image and HST images. The SINFONI and HST images were aligned on the tip of the knot. Log intensity scale is used for all of the images. The size of the image is 22.3 × 8.5 arcsec2.

The [O iii] image shows the knot in absorption; the tip is slightly off the peak from [N ii] images (Fig. 9). This has also been found by O'Dell & Henney (2000) for other knots.

Figure 9

Cross-cut of Fig. 8 along the long axis.

Figure 9

Cross-cut of Fig. 8 along the long axis.

A cross-section of the H2v= 1–0 S(1) and [N ii]+ Hα images shows that the decay of the intensities towards the tail is very fast (almost immediate) for the ionized lines, and slower for the H2v= 1–0 S(1). The main ionized region is a thin layer at the tip; the majority of the material remains molecular or neutral.

3.2 Spectra

Fig. 10 shows the spectra of the knot K1 at 12 regions indicated in Fig. 11. Within each region of 5 × 5 pixel (except region (a) which has 5 × 4 pixel), the SINFONI data have been averaged. At most 12 H2 lines (three of them with low signal-to-noise ratio) are detected by SINFONI. The intensities are summarized in Table 2. The strongest detected line is the 1.95 μm H2v= 1–0 S(3), and the 2.12 μm H2v= 1–0 S(1) and 2.4 μm v= 1–0 Q branches are also strong. The H2 lines are unresolved at the resolution of R= 5090. The 2.07 μm v= 2–1 S(3), 2.15 μm v= 2–1 S(2) and 2.20 μm v= 3–2 S(3) lines are only marginally detected.

Figure 10

Spectra within the knot K1 at 12 0.675 × 0.5-arcsec2 areas defined in Fig. 11. The y-axis shows the spectral intensity from −0.5 × 108 to 6 × 108 Jy sr−1. The identifications of the H2 transitions are indicated in panel (a).

Figure 10

Spectra within the knot K1 at 12 0.675 × 0.5-arcsec2 areas defined in Fig. 11. The y-axis shows the spectral intensity from −0.5 × 108 to 6 × 108 Jy sr−1. The identifications of the H2 transitions are indicated in panel (a).

Figure 11

The 12 regions shown by boxes on the 2.12-μm image. The spectra are averaged within that area, which corresponds to the diagram in Fig. 12. The right-hand top box is the area used to estimate the error of the intensities.

Figure 11

The 12 regions shown by boxes on the 2.12-μm image. The spectra are averaged within that area, which corresponds to the diagram in Fig. 12. The right-hand top box is the area used to estimate the error of the intensities.

Table 2

Intensities of H2 lines at areas (a)–(c) and ratios with respect to the v= 2–1 S(1) line.

Wavelength Transition Upper state energy Statistical weight Intensity Iν× 107 Erra Obs ratiob 
(a) (b) (c)  (a) (b) (c) 
(μm)  (K) (cm−1 (W m−2 sr−1 
1.958 v= 1–0 S(3)c 8365 5813 33 4.10 2.35 2.96 0.10 220 226 223 
2.004 v= 2–1 S(4) 14764 10 262 13 <0.40a  
2.034 v= 1–0 S(2) 7584 5271 0.67 0.37 0.49 0.04 36 35 36 
2.073 v= 2–1 S(3) 13890 9654 33 0.08d   0.09   
2.128 v= 1–0 S(1) 6956 4834 21 1.86 1.04 1.32 0.07 100 100 100 
2.154 v= 2–1 S(2) 13150 9139 0.07d   0.08   
2.201 v= 3–2 S(3) 19086 13 265 33 0.02d   0.03  
2.224 v= 1–0 S(0) 6471 4497 0.42 0.24 0.31 0.06 22 23 23 
2.248 v= 2–1 S(1) 12550 8722 21 0.18 0.09 0.12 0.04 
2.386 v= 3–2 S(1) 17818 12 384 21 <0.09a  
2.407 v= 1–0 Q(1)c 6149 4273 1.84 1.06 1.30 0.23 99 102 97 
2.413 v= 1–0 Q(2)c 6471 4497 0.55 0.29 0.39 0.12 29 28 29 
2.424 v= 1–0 Q(3)c 6956 4834 21 1.85 1.03 1.27 0.14 99 99 96 
2.438 v= 1–0 Q(4)c 7586 5272 0.57 0.31 0.38 0.18 30 30 28 
Wavelength Transition Upper state energy Statistical weight Intensity Iν× 107 Erra Obs ratiob 
(a) (b) (c)  (a) (b) (c) 
(μm)  (K) (cm−1 (W m−2 sr−1 
1.958 v= 1–0 S(3)c 8365 5813 33 4.10 2.35 2.96 0.10 220 226 223 
2.004 v= 2–1 S(4) 14764 10 262 13 <0.40a  
2.034 v= 1–0 S(2) 7584 5271 0.67 0.37 0.49 0.04 36 35 36 
2.073 v= 2–1 S(3) 13890 9654 33 0.08d   0.09   
2.128 v= 1–0 S(1) 6956 4834 21 1.86 1.04 1.32 0.07 100 100 100 
2.154 v= 2–1 S(2) 13150 9139 0.07d   0.08   
2.201 v= 3–2 S(3) 19086 13 265 33 0.02d   0.03  
2.224 v= 1–0 S(0) 6471 4497 0.42 0.24 0.31 0.06 22 23 23 
2.248 v= 2–1 S(1) 12550 8722 21 0.18 0.09 0.12 0.04 
2.386 v= 3–2 S(1) 17818 12 384 21 <0.09a  
2.407 v= 1–0 Q(1)c 6149 4273 1.84 1.06 1.30 0.23 99 102 97 
2.413 v= 1–0 Q(2)c 6471 4497 0.55 0.29 0.39 0.12 29 28 29 
2.424 v= 1–0 Q(3)c 6956 4834 21 1.85 1.03 1.27 0.14 99 99 96 
2.438 v= 1–0 Q(4)c 7586 5272 0.57 0.31 0.38 0.18 30 30 28 

a 3σ of the noise level of the intensity in the error region indicated in Fig. 11.

bLine ratio with respect to the 2.128 μm v= 1–0 S(1) line.

cThese lines have a large (∼30 per cent) error in relative intensity calibration due to the influence of H2O in the terrestrial atmosphere. They are excluded from the comparison with models.

dMarginal detections.

Several high transition lines within this wavelength range are not detected, such as the 2.00 μm v= 2–1 S(4), 2.38 μm v= 3–2 S(1). The Brγ line is not detected.

3.2.1 Energy diagram

Fig. 12 shows the energy diagram of the H2 lines for several regions in the knot indicated in Fig. 11. Einstein coefficients from Turner, Kirby-Docken & Dalgarno (1977) are used. The slopes in the diagrams show that the line intensities follow a T= 1800 K local thermodynamic equilibrium (LTE) distribution. At the bright area (a)–(c), the observed line intensities follow the 1800 K LTE line up to the upper energy of 8000 cm−1. The systematic uncertainty in the absolute H2 intensity (up to 50 per cent) affects the column density, but not the excitation temperature which is determined by the slope.

Figure 12

The energy diagrams for area (a)–(l) defined in Fig. 11; the column density for a given J upper level divided by the statistical weight as a function of the upper state energy in cm−1. The square shows the measured energy levels. The thick lines show the LTE case for 1800 K and for column densities as given in the diagrams. For a comparison, we plot the 900 K LTE line, as derived for knots in the outer region of the nebula (Cox et al. 1998) in (a). The column density for the 900 K line is 8 × 1018 cm−2. This temperature cannot fit the H2 line intensities measured in the knot K1.

Figure 12

The energy diagrams for area (a)–(l) defined in Fig. 11; the column density for a given J upper level divided by the statistical weight as a function of the upper state energy in cm−1. The square shows the measured energy levels. The thick lines show the LTE case for 1800 K and for column densities as given in the diagrams. For a comparison, we plot the 900 K LTE line, as derived for knots in the outer region of the nebula (Cox et al. 1998) in (a). The column density for the 900 K line is 8 × 1018 cm−2. This temperature cannot fit the H2 line intensities measured in the knot K1.

3.3 Line-ratio map

Fig. 13 shows the line-ratio maps within the knot. Fig. 13(a) maps the rotational temperature variations within the knot, represented by the 2.03 μm v= 1–0 S(2) and 2.12 μm v= 1–0 S(1) lines. This rotational temperature is uniform within the errors throughout the knot. This uniform rotational temperature is expected from the energy diagram (Fig. 12), because all of the line intensities follow 1800 K LTE in any area.

Figure 13

The line-ratio maps of the cometary knot K1. The contour shows the surface brightness of 2.12 μm H2v= 1–0 S(1) line at 0.2 × 10−7, 0.5 × 10−7 and 1 × 10−7, 2 × 10−7W m−2 sr−1.

Figure 13

The line-ratio maps of the cometary knot K1. The contour shows the surface brightness of 2.12 μm H2v= 1–0 S(1) line at 0.2 × 10−7, 0.5 × 10−7 and 1 × 10−7, 2 × 10−7W m−2 sr−1.

The vibrational temperature seems to vary within the knot but this is within the uncertainty. Fig. 13(b) shows the line ratio of 2.24 μm H2v= 2–1 S(1) and 2.12 μm H2v= 1–0 S(1). This is the only combination to obtain the vibrational temperature within our observed data. The line ratio tends to be highest at the tip (∼0.1) and to decrease towards the tail, although a careful treatment of v= 2–1 S(1) lines is needed.

4 DISCUSSION

4.1 Excitation diagrams and temperatures

The H2 excitation diagrams are fitted by a single LTE temperature of 1800 K. This is much higher than that of Cox et al. (1998) who obtained 900 K by fitting pure-rotational lines up to the S(7) transition. The region observed by Cox et al. (1998) is located at the western rim of the nebula, and is 5–6 arcmin away from the central star. The pixel size of their ISOCAM data was 6 arcsec and emission from multiple knots contributed to each single pixel. In contrast, our target is a single, isolated knot located at the innermost region of the flock of knots (2.5 arcmin from the central star).

O'Dell, Henney & Ferland (2007) also obtained an excitation temperature of 988 K from 5- to 15-μm spectra in the outer part of the nebula. O'Dell et al. (2007) state that the distance of those slit positions is similar to that of Cox et al. (1998). Although they do not provide detailed information on the slit positions and observing mode for their two Spitzer spectra, the Spitzer archive can provide this, suggesting that their two slit positions are 5.6 and 4.2 arcmin from the central star, and the slit size is 3.6 × 57 arcsec2. Further three spectra at different slit positions are available in the archive, but these do not fit the description of the data in O'Dell et al. (2007).

The difference in measured temperatures suggests that the excitation temperature of H2 is not uniform within the Helix Nebula: the H2 molecules reach higher temperatures within the inner region. From about 2.5–5 arcmin away from the central star, the excitation temperature decreases from 1800 to 900–1000 K. This provides evidence for temperature variations within the nebula.

Hora et al. (2006) show that the [3.6]–[4.5] versus [4.5]–[8.0] colour varies within the nebula. All three bands are dominated by H2 lines. Knots located at the inner rim of the main nebula are brighter in the 4.5-μm band. The strongest expected line in this band is the 4.69 μm H2v= 0–0 S(9), whose upper energy is the highest among the dominant H2 lines within the IRAC filters. The colour–colour diagram of Hora et al. (2006) also suggests a higher excitation temperature in the inner region, and global variation in the excitation temperature in the entire nebula. An analysis of spectra with several slit positions within a nebula shows that the H2 temperature is not uniform within a PN (Hora, Latter & Deutsch 1999; Davis et al. 2003). Excitation temperature variations appear normal within a single PN.

Furthermore, H2 excitation temperatures in PNe have been found to be as high as 2000 K (Hora et al. 1999; Davis et al. 2003) and lower than 1000 K (Cox et al. 1998; Bernard-Salas & Tielens 2005; Matsuura & Zijlstra 2005a). Variations in excitation temperatures both between PNe and within a single PN appear to be normal.

4.2 Column density

The H2 line intensities are fitted using column densities in the range of 1 × 1017–8 × 1017 cm−2. This range is smaller than the Cox et al. (1998) measurements of 3 × 1018 cm−2. Our target is an isolated knot, while the low spatial resolution of the ISOCAM data almost included multiple knots within the field of view, hence the H2 intensity is much higher (Speck et al. 2002).

The column density of H2 can be converted to a hydrogen mass of 2 × 10−8 M. Here, we assume that the knot has a column density of 4 × 1017 cm−2 (i.e. to emit average intensity over 2 × 2 arcsec2 at the excitation temperature of 1800 K), the distance is 219 pc, the dimension of the knot is 2 × 2 arcsec2 and the density is uniform within this area. The estimated hydrogen mass is a factor of 1000 less than the estimate of O'Dell & Handron (1996), who used the extinction of the [O ii] line as a mass tracer. Our infrared H2 lines trace only highly excited H2, as expected from the upper-state energy (>6000 K). Colder H2 gas is inefficient at emitting these lines (Cox et al. 1998).

In order to measure the mass of cold H2 gas more directly, we need observations at UV wavelengths, where H2 lines could be found in absorption. However, this approach may be compromised by the contribution to H2 absorption by the interstellar medium. Adopting the hydrogen mass of O'Dell & Handron (1996) with a comparison of our estimated H2 mass indicates that H2 is heated only at the surface, but in fact H2 is present throughout the knot. This favours a scenario where the detected H2 was already present within the knot, that is, it is not necessary to assume that it formed from chemical reactions from atomic/neutral hydrogen within this surface. However, this argument is based on an expected correlation between dust extinction and H2. A direct detection is required to confirm the presence of a large, cold H2 reservoir.

4.3 Excitation mechanisms of molecular hydrogen

The cometary knot K1 emits a 1–0 S(1) line intensity of 2 × 10−7 W m−2 sr−1. The adopted uncertainty is a factor of 2. The 2–1/1–0 S(1) line ratio is ∼0.1 ± 0.02 at the tip, using the uncertainty on the response correction.

Burton, Hollenbach & Tielens (1992) calculated the line intensities of 1–0 S(1) and 2–1 S(1) lines for J-type shocks, C-type shocks and in PDR. We found that within their model the measured line intensities and ratios can be fitted equally well under several model conditions.

  • A PDR heated by UV radiation where the density is n= 106 cm−3 and the UV strength is G0= 1.2 × 104 (within the range of G0= 1–1.2 × 104)

  • C-type shocks with an upstream density n0= 104 cm−3 and shock velocity vs∼ 27 km s−1 (within the range of 27–28 km s−1).

  • J-type shocks n0= 106 cm−3 and shock velocity vs∼ 9 km s−1 (9–10 km s−1).

Although there is some uncertainty in absolute intensity, the line ratio is the strongest constraint on the above conditions.

Meaburn et al. (1998) estimated the molecular hydrogen density of another knot to be 8.9 × 105 cm−3 using the extinction in the [O iii] 5007 Å line. This knot appears brighter than K1, and larger in radius when observed in the [N ii] line. We follow their method to estimate the density of the knot K1. The absorption at [O iii] is 0.73 with respect to the continuum (Section 3.1.2). This corresponds to an extinction coefficient c= 0.15, E(BV) = 0.14 mag, and an H2 column density of 4.0 × 1020 cm−2. If the diameter of the knot is 1.5 arcsec, an H2 number density of 8 × 104 cm−3 is obtained for a distance of 219 pc. The derived H2 density is consistent for the PDR model of H2 excitation in Burton et al. (1992).

The far-UV (6–13.6 eV) flux at the knot K1 is about G0= 8, where G0 is the far-UV radiation measured in units of the Habing (1968) flux. This is based on Su et al.'s (2007) estimate assuming a luminosity of the central star of 76 L and a distance of 219 pc. The required UV radiation in Burton et al.'s (1992) model is G0 > 1 × 104, which is an order of magnitude higher than the estimated UV radiation field strength at the knot K1. We used the UCL (University College London) PDR model (Bell et al. 2005) to calculate the conditions independently. At a UV radiation field of G0= 8, we obtain a temperature below 100 K. Röllig et al. (2007) compare benchmark calculations of independent PDR codes, including the UCL-PDR model and Tielens & Hollenbach's (1985) model that was incorporated in Burton et al.'s (1992) H2 model. They find consistent gas temperatures among PDR models in their benchmark calculations. These results suggest that the PDR models can reproduce the measured LTE gas temperature (1800 K) of the H2 lines in the knot K1 only, if the UV radiation strength is increased. A similar conclusion is derived by Cox et al. (1997) and O'Dell, Henney & Ferland (2005). The value for G0 is defined as the flux between 6 and 13.6 Å a narrow-band UV radiation field, adopted for interstellar radiation field. If we consider the continuous stellar spectrum of the central star, the UV flux increases by a factor of 10 (O'Dell et al. 2007). However, this remains a factor of 250 short of the required flux.

The speed of ambient gas for C-type shocks is vs∼ 27 km s−1 to fit the H2 line intensities and line ratios, from theoretical work by Burton et al. (1992). The required velocity can vary by ∼±10 km s−1 depending on the assumed magnetic field strength and the iron fraction. The [He ii] and [O iii] lines show an expansion velocity of 13 km s−1 near the central star (Meaburn et al. 2005). Within an expanding nebula, hydrodynamic effects will cause significant velocity gradients (Schönberner, Jacob & Steffen 2005), as are observed in PNe (Gesicki, Acker & Zijlstra 2003). The overpressure of the ionized region dominates, and (if present) the pressure from the inner, hot bubble might be added. The same processes will occur for each knot at the ionized, facing edge. Meaburn et al. (1998, 2005) postulate turbulent velocities ≥10 km s−1 (i.e. larger than the sound speed). A C-type shock velocity could be associated with such motion. The gas density of PNe is typically n0∼ 104 cm−3. This is consistent with the required upstream density. C-type shock excitation of H2 is possible. Stronger observational constraints on the velocity structure of the knot would be helpful.

The presence of magnetic fields has been reported in several young or pre-PNe using submillimetre polarization (Sabin, Zijlstra & Greaves 2007). They find a magnetic field of ∼1 mG at 5 × 1016 cm from the central star in other PNe. The Helix knots are located 10 times farther from the star than their measured location. A dipole field would decay as r−3: this would leave a negligible field in the Helix Nebula. A solar-type field decays as r−2, and a frozen toroidal field (as favoured by Sabin et al. 2007) may decay slower with radius. The formation of a knot may strengthen after its embedded magnetic field. The field required for the C-type shock is plausible within the knot, compared to the stronger fields detected in more compact shells. The interknot medium is likely to show a weaker field.

An upstream (wind) density of 106 cm−3 is required for the J-type shock model. Although the density within knots themselves is recorded at 106 cm−3 (O'Dell & Handron 1996; Meaburn et al. 1998), it is unlikely that the upstream region has such a high density.

5 CONCLUSIONS

We have investigated the detailed structure of a single knot close to the inner edge of the main ring of the Helix Nebula.

We find that the rotational-vibrational temperature of H2 is as high as 1800 K for this innermost cometary knot. The rotational temperature is uniform within the knot, and the vibrational temperature appears to follow the same distribution except for a possible decrease towards the tail. The derived temperature is much higher than previously measured (900 K) for knots in the outer region. The excitation temperature changes with radial distance from the central star. The studied knot has a wide head, with H2 distributed in a crescent.

We examine the possible molecular hydrogen excitation mechanisms. Based on the line intensities and ratios, C-type shocks can provide a fit using plausible local conditions, although the required velocity is slightly higher than the observed one. This excitation requires the presence of an as-yet-undetected magnetic field. A J-type shock model does not fit. We also tested the possibility that H2 lines are excited in PDR, but PDR models have difficulties to reproduce the very high temperature, unless the UV field is increased by two orders of magnitude over the stellar radiation field. A further test of the models will require observations of the velocity structure of the head and tail. We also lack a synthesis model combining collisional and UV excitation, with hydrodynamical interactions.

We appreciate technical support from the ESO staff during the observations and the data analysis. MM appreciates encouragement from Prof. Arimoto for this study. MM is grateful for hospitality at the UCL and SAAO during the visits. A discussion with Dr M. Cohen in early stages of this research was very useful.

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Author notes

*
Based on observations with the European Southern Observatory, Very Large Telescope with an instrument, SINFONI (the proposal numbers: 076.D-0807).